Could someone help explain this problem to me . . .
Carbon 14 has a half-life of 5700 year, scientist use this fact to determine the age of things made of organic material. Suppose the average page of a book containing aprox. 0.5mg of Carbon 14 is put into a time capsule how much carbon 14 will each page contain after each of the following number of years. A. 5,700 B. 11,400 C. 22,800 D. 34,200
How do I go about this?
Well, we know that half of it will change into another form in 5700 years, so if you start with .5 mg than in 5,700 years you would have half or .25 mg. 11,400 is another half life so half of .25 = .125 mg. 22,800 is two more half lives so half .125 twice.
How old is the bone? Ifthere are 10 grams of C14 for every 1000 grams of bone?
To solve this problem, you need to understand the concept of half-life and how it applies to Carbon-14 decay. The half-life of Carbon-14 is given as 5700 years, which means that after 5700 years, half of the Carbon-14 atoms in a sample will have decayed.
To calculate the amount of Carbon-14 remaining after a given number of years, you can use the formula:
Remaining amount = Initial amount x (1/2)^(number of half-lives)
Here's how you can approach each part of the problem:
A. After 5,700 years (1 half-life):
- Start with an initial amount of 0.5mg of Carbon-14.
- Since it goes through 1 half-life, divide the initial amount by 2.
- Calculate: 0.5mg * (1/2)^1 = 0.25mg
So, after 5,700 years, each page would contain approximately 0.25mg of Carbon-14.
B. After 11,400 years (2 half-lives):
- Start with an initial amount of 0.5mg.
- Since it goes through 2 half-lives, divide the initial amount by 2 twice.
- Calculate: 0.5mg * (1/2)^2 = 0.125mg
So, after 11,400 years, each page would contain approximately 0.125mg of Carbon-14.
C. After 22,800 years (4 half-lives):
- Start with an initial amount of 0.5mg.
- Since it goes through 4 half-lives, divide the initial amount by 2 four times.
- Calculate: 0.5mg * (1/2)^4 = 0.03125mg
So, after 22,800 years, each page would contain approximately 0.03125mg of Carbon-14.
D. After 34,200 years (6 half-lives):
- Start with an initial amount of 0.5mg.
- Since it goes through 6 half-lives, divide the initial amount by 2 six times.
- Calculate: 0.5mg * (1/2)^6 = 0.0078125mg
So, after 34,200 years, each page would contain approximately 0.0078125mg of Carbon-14.
Remember, this calculation assumes that there is no additional Carbon-14 being introduced into the system.